D. ant plane

D. ant plane

A single point of time: 2.0 sec

Memory Limit: 512 MB

There are a plane  n ants, it can be regarded as the path traveled in a straight line

By these n  certain regions defined straight lines is unbounded, while other regions are bounded.

The maximum number of bounded region is how much?

Example, there are four straight lines, only the following bounded region leftmost figure is the largest line defined

Input Format

T  set of inputs,  ( . 1 ≤ T ≤ 100 )

Each a number of  n-  , ( . 1 ≤ n- ≤ 10 . 9 )

Output Format

For each test, it outputs a maximum integer number of bounded areas.

Sample

input

1
4

output

3

 Common math problems to find the law 

1   0

2   0

3   1

4   3

5   6

6  10

Can be calculated using the arithmetic formula, is the value of n (n-1) / 2 entries equal to the arithmetic and 4, the first three values ​​in the first term is equal to 5 and so the difference of the front four. . . .

AC Code:

#include<iostream>
using namespace std;
typedef long long ll;
int main(){
    int t;
    cin>>t;
    while(t--){
        ll n;
        cin>>n;
        if(n==1||n==2){
            cout<<0<<endl;
        }
        else{
            n--;
            cout<<n*(n-1)/2<<endl;
        }
    }
    return 0;
}

 Similar problems are summarized:

1 Title: n straight line, a plane can be divided into a maximum number of regions.

    Formula: B (n) = n (n + 1) / 2 + 1, or F (n) = F (n-1) + n

2  has a plane of X n type unknown object, such that the plane formed by division as much as possible

　　Formula   f = N (2N + 1) +1

 

3  . Division planes polyline

Can be seen from the figure, an extra fold line each, a plurality will be 4 * (n-1) points of intersection, will be more than that is 4 * (n-1) +1 planar, then we can get the recursive formula:

       f [n] = f [n-1] + 4 * (n-1) +1 or 2 * n ^ 2-n + 1